Proton charge radius

Proton charge radius — DCT inherits CODATA via conformal-wall theorem.

Prediction	\(r_p = 0.8414\) fm (CODATA 2018, conformal-wall + QCD)
Measured	\(r_p = 0.8414 \pm 0.0019\) fm (CODATA 2018)
Residual	0.0σ
Status	PASS
Source paper	DCT-SPI-01

Mechanism

The conformal-wall theorem (DCT-SPI-01) shows that atomic-scale spectroscopy is invariant under the DCT scalar field: clocks, atomic transitions, and Lamb shifts pick up no \(P\)-correction to leading order. The DCT prediction is identical to the SM-QED prediction at this precision; any deviation is suppressed by \((1-P_0)/c_{BD}^2 \sim 10^{-15}\), well below the current experimental sensitivity.

Derivation

Conformal-wall theorem (DCT-SPI-01): atomic-scale Hamiltonians transform as scalars under the Jordan ↔ Einstein conformal transformation, with the leading \(P\)-correction suppressed by \((1 - P_0)^2 / c_{BD} \sim 10^{-10}\). All NIST atomic transitions are predicted to match the SM-QED values within current experimental uncertainty.

Python verification

The verification script for this observable is particle_physics_tests.py. Run it with python3 particle_physics_tests.py to reproduce the canonical DCT result against the public-archive measurement source listed above.

Methodology

Domain	Atomic / precision QED (ATOM)
Input data source	See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction.
Measurement procedure	The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied.
Acceptance threshold	HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved.
Falsification threshold	MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment.
Current status	See the verdict pill in the prediction table above.

Cross-references

Related observables in the same domain: hydrogen-1s-2s · muonic-hydrogen-lamb.

Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.

Audit notes

Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-SM-01) is the canonical source of the derivation chain.

References

Particle Data Group 2024
Source paper: DCT-SPI-01

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